Examples of PDEs all whose points are characteristic

Let π : FM ! M be the bundle of linear frames of a manifold M. A basis Lijk , j < k, of diffeomorphism invariant Lagrangians on J1 (FM) was determined in [J. Muñoz Masqué, M. E. Rosado, Invariant variational problems on linear frame bundles, J. Phys. A35 (2002) 2013-2036]. The notion of a characteristic hypersurface for an arbitrary first-order PDE system on an ar- bitrary bred manifold π : P → M, is introduced and for the systems dened by the Euler-Lagrange equations of Lijk every hypersurface is shown to be characteristic. The Euler-Lagrange equations of the natural basis of Lagrangian densities Lijk on the bundle of linear frames of a manifold M which are invariant under diffeomorphisms, are shown to be an underdetermined PDEs systems such that every hypersurface of M is characteristic for such equations. This explains why these systems cannot be written in the Cauchy-Kowaleska form, although they are known to be formally integrable by using the tools of geometric theory of partial differential equations, see [J. Muñoz Masqué, M. E. Rosado, Integrability of the eld equations of invariant variational problems on linear frame bundles, J. Geom. Phys. 49 (2004), 119-155]

The Minimum Number of Points Taking Part in k-Sets in Sets of Unaligned Points

En este trabajo se da un ejemplo de un conjunto de n puntos situados en posición general, en el que se alcanza el mínimo número de puntos que pueden formar parte de algún k-set para todo k con 1menor que=kmenor quen/2. Se generaliza también, a puntos en posición no general, el resultado de Erdõs et al., 1973, sobre el mínimo número de puntos que pueden formar parte de algún k-set. The study of k- sets is a very relevant topic in the research area of computational geometry. The study of the maximum and minimum number of k-sets in sets of points of the plane in general position, specifically, has been developed at great length in the literature. With respect to the maximum number of k-sets, lower bounds for this maximum have been provided by Erdõs et al., Edelsbrunner and Welzl, and later by Toth. Dey also stated an upper bound for this maximum number of k-sets. With respect to the minimum number of k-set, this has been stated by Erdos el al. and, independently, by Lovasz et al. In this paper the authors give an example of a set of n points in the plane in general position (no three collinear), in which the minimum number of points that can take part in, at least, a k-set is attained for every k with 1 ≤ k < n/2. The authors also extend Erdos’s result about the minimum number of points in general position which can take part in a k-set to a set of n points not necessarily in general position. That is why this work complements the classic works we have mentioned before.

Optimal fits of diffusion constants from single-time data points of Brownian trajectories

Experimental methods based on single particle tracking (SPT) are being increasingly employed in the physical and biological sciences, where nanoscale objects are visualized with high temporal and spatial resolution. SPT can probe interactions between a particle and its environment but the price to be paid is the absence of ensemble averaging and a consequent lack of statistics. Here we address the benchmark question of how to accurately extract the diffusion constant of one single Brownian trajectory. We analyze a class of estimators based on weighted functionals of the square displacement. For a certain choice of the weight function these functionals provide the true ensemble averaged diffusion coefficient, with a precision that increases with the trajectory resolution.

Decelerator elements for ramp transfer points in fruit packing lines

Two different decelerator elements used to reduce impacts on fruits on ramp transfer points in fruit packing lines were designed and tested. The performance of these elements, a powered decelerator and a multiple curtain, was compared to commercial decelerators (blankets). A ramp of length 60 cm was placed at an angle of 30º in an experimental fruit packing line between a roller transporter and a conveyor. The decelerators were placed on top of the ramp. Different tests were carried out to study the performance of the decelerators using instrumented spheres (IS 100) of various sizes. Results showed that decelerators can reduce the impact intensity down to safe thresholds. The powered decelerator was the most effective because it reduced the speed of fruits and did not cause retention of the fruit, when correctly regulated.

Perfect imaging of three object points with only two analytic lens surfaces in two dimensions

In this work, a new two-dimensional analytic optics design method is presented that enables the coupling of three ray sets with two lens profiles. This method is particularly promising for optical systems designed for wide field of view and with clearly separated optical surfaces. However, this coupling can only be achieved if different ray sets will use different portions of the second lens profile. Based on a very basic example of a single thick lens, the Simultaneous Multiple Surfaces design method in two dimensions (SMS2D) will help to provide a better understanding of the practical implications on the design process by an increased lens thickness and a wider field of view. Fermat?s principle is used to deduce a set of functional differential equations fully describing the entire optical system. The transformation of these functional differential equations into an algebraic linear system of equations allows the successive calculation of the Taylor series coefficients up to an arbitrary order. The evaluation of the solution space reveals the wide range of possible lens configurations covered by this analytic design method. Ray tracing analysis for calculated 20th order Taylor polynomials demonstrate excellent performance and the versatility of this new analytical optics design concept.

Passing or stopping by: meeting points on the fly

In traditional nomadic societies, social life was created around mobile points rekindled in different places each time. After the settled urbanization period, where social life centred on fixed attractions, we are opening a new era, where thanks to technology, we are able to create meeting points on the fly. Contemporary public space for passer-by users will be again based on traces instead of lines, reflecting current reality far more accurately.

Analytical Calculation of Stall-inception and Surge Points for an Axial-flow Compresor Rotor

Recently, a theoretical criterion to calculate the stability of an axial-flow compressor rotor has been presented in the scientific literature. This theoretical criterion was used for determining the locus of the stability line over the rotor map and for predicting the post-stall evolution of the constant-speed line of a rotor. The main objective of this paper is to improve the predictions of such a model. To do that, the paper proposes a different characterization of the characteristic azimuthal length and a calculation of the ratio of specific heats based on a polytropic exponent. Thanks to these new values, the model predicts two bifurcation points in the behaviour of the flow: the inception point of the instability and the surge point. Experimental data from a pure axial compressor are used to validate the model showing that the prediction of the flow coefficient at the surge point has an error inferior to 5%. For the rotor studied, the paper provides a quantitative and qualitative description of the inception of the instability and of the mechanism involved in the instable region of the compressor map. The paper also discusses the role of rotor efficiency in the position of the bifurcations and gives a sensitivity analysis of its position. Finally, it presents a discussion about how the model can explain the different behaviours exhibited by the same rotor when the flow coefficient is reduced

Meromorphic continuation of functions and arbitrary distribution of interpolation points

We characterize the region of meromorphic continuation of an analytic function ff in terms of the geometric rate of convergence on a compact set of sequences of multi-point rational interpolants of ff. The rational approximants have a bounded number of poles and the distribution of interpolation points is arbitrary.

Sharp imaging of Multiple object pointS: how and why

Is it possible to sharply image M object points with N surfaces when N menor que M? Under what conditions? Why is it interesting for optimization? What is the role of the SMS method?

Concept of operations for ATM by managing uncertainty through multiple metering points

This paper presents an operational concept for Air Traffic Management, and in particular arrival management, in which aircraft are permitted to operate in a manner consistent with current optimal aircraft operating techniques. The proposed concept allows aircraft to descend in the fuel efficient path managed mode and with arrival time not actively controlled. It will be demonstrated how the associated uncertainty in the time dimension of the trajectory can be managed through the application of multiple metering points strategically chosen along the trajectory. The proposed concept does not make assumptions on aircraft equipage (e.g. time of arrival control), but aims at handling mixed-equipage scenarios that most likely will remain far into the next decade and arguably beyond.

Un modelo de relación entre los programas de innovación abierta y la creación de valor

En un mundo donde el cambio es constante y cada vez más vertiginoso, la innovación es el combustible que utilizan las empresas que permite su renovación constante y, como consecuencia, su supervivencia en el largo plazo. La innovación es sin dudas un elemento fundamental para determinar la capacidad de las empresas en crear valor a lo largo del tiempo, y por ello, las empresas suelen dedicar esfuerzos considerables y recursos de todo tipo para identificar nuevas alternativas de innovación que se adapten a su estrategia, cultura, objetivos y ambiciones corporativas. Una forma específica para llevar a cabo la innovación es la innovación abierta. Esta se entiende como la innovación que se realiza de manera conjunta con otras empresas o participantes del ecosistema. Cabe la aclaración que en este documento se toma la definición de ecosistema referida al conjunto de clientes, proveedores, competidores y otros participantes que interactúan en un mismo entorno donde existen posiciones de liderazgo que pueden cambiar a lo largo del tiempo (Moore 1996). El termino de innovación abierta fue acuñado por Henry Chesbrough hace algo mas de una década para referirse a esta forma particular de organizar la innovación corporativa. Como se observa en el presente trabajo la innovación abierta es un nuevo paradigma que ha capturado el interés académico y empresarial desde algo más de una década. Se verán varios casos de innovación abierta que se están llevando a cabo en diversos países y sectores de la economía. El objetivo principal de este trabajo de investigación es el de desarrollar y explicar un modelo de relación entre la innovación abierta y la creación de valor en las empresas. Para ello, y como objetivos secundarios, se ha investigado los elementos de un Programa de Innovación Abierta, los impulsores 1 de creación de valor, el proceso de creación de valor y, finalmente, la interacción entre estos tres elementos. Como producto final de la investigación se ha desarrollado un marco teórico general para establecer la conexión entre la innovación abierta y la creación de valor que facilita la explicación de la interacción entre ambos elementos. Se observa a partir de los casos de estudio que la innovación abierta puede abarcar todos los sectores de la economía, múltiples geografías y empresas de distintos tamaños (grandes empresas, pequeñas y medianas empresas, incluso empresas de reciente creación) cada una de ellas con distinta relevancia dentro del ecosistema en el que participan. Elementos de un Programa de Innovación Abierta La presente investigación comienza con la enumeración de los distintos elementos que se encuentran presentes en los Programas de Innovación Abierta. De esta manera, se describen los diversos elementos que se han identificado a través de la revisión de la literatura académica que se ha llevado a cabo. En función de una serie de características comunes, los distintos elementos se agrupan en cuatro niveles diferentes para lograr un mejor entendimiento de los Programas de Innovación Abierta. A continuación se detallan estos elementos § Organización del Programa. En primer lugar se menciona la existencia de una estructura organizativa capaz de cumplir una serie de objetivos establecidos previamente. Por su naturaleza de innovación abierta deberá existir cierto grado de interacción entre los distintos miembros que participen en el proceso de innovación. § Talento Interno. El talento interno asociado a los programas de innovación abierta juega un rol fundamental en la ejecución y éxito del programa. Bajo este nivel se asocian elementos como la cultura de innovación abierta y el liderazgo como mecanismo para entender uno de los elementos que explica el grado de adopción de innovación en una empresa. Estrechamente ligados al liderazgo se encuentran los comportamientos organizacionales como elementos diferenciadores para aumentar las posibilidades de creación de innovación abierta. § Infraestructura. En este nivel se agrupan los elementos relacionados con la infraestructura tecnológica necesaria para llevar a cabo el programa incluyendo los procesos productivos y las herramientas necesarias para la gestión cotidiana. § Instrumentos. Por último, se mencionan los instrumentos o vehículos que se utilizan en el entorno corporativo para implementar innovación abierta. Hay varios instrumentos disponibles como las incubadoras corporativas, los acuerdos de licenciamiento o las áreas de capital de riesgo corporativo. Para este último caso se hará una mención especial por el creciente y renovado interés que ha despertado tanto en el entorno académico como empresarial. Se ha identificado al capital de riesgo corporativo como un de los elementos diferenciales en el desarrollo de la estrategia de innovación abierta de las empresas ya que suele aportar credibilidad, capacidad y soporte tecnológico. Estos cuatro elementos, interactuando de manera conjunta y coordinada, tienen la capacidad de crear, potenciar e incluso desarrollar impulsores de creación de valor que impactan en la estrategia y organización de la empresa y partir de aquí en su desempeño financiero a lo largo del tiempo. Los Impulsores de Creación de Valor Luego de identificar, ordenar y describir los distintos elementos presentes en un Programa de Innovación Abierta se ha avanzado en la investigación con los impulsores de creación de valor. Estos pueden definirse como elementos que potencian o determinan la capacidad de crear valor dentro del entorno empresarial. Como se puede observar, se detallan estos impulsores como punto de interacción entre los elementos del programa y el proceso de creación de valor corporativo. A lo largo de la presente investigación se han identificado 6 impulsores de creación de valor presentes en un Programa de Innovación Abierta. § Nuevos Productos y Servicios. El impulsor de creación de valor más directo y evidente en un Programa de Innovación Abierta es la capacidad de crear nuevos productos y servicios dado que se relacionan directamente con el proceso de innovación de la empresa § Acceso a Mercados Adyacentes. El proceso de innovación también puede ser una fuente de valor al permitir que la empresa acceda a mercados cercanos a su negocio tradicional, es decir satisfaciendo nuevas necesidades de sus clientes existentes o de nuevos clientes en otro mercado. § Disponibilidad de Tecnologías. La disponibilidad de tecnologías es un impulsor en si mismo de la creación de valor. Estas pueden ser tanto complementarias como de apalancamiento de tecnologías ya existentes dentro de la empresa y que tengan la función de transformar parte de los componentes de la estrategia de la empresa. § Atracción del Talento Externo. La introducción de un Programa de Innovación Abierta en una empresa ofrece la oportunidad de interactuar con otras organizaciones del ecosistema y, por tanto, de atraer el talento externo. La movilidad del talento es una característica singular de la innovación abierta. § Participación en un Ecosistema Virtuoso. Se ha observado que las acciones realizadas en el entorno por cualquiera de los participantes también tendrán un claro impacto en la creación de valor para el resto de participantes por lo tanto la participación en un ecosistema virtuoso es un impulsor de creación de valor presente en la innovación abierta. § Tecnología “Dentro--‐Fuera”. Como último impulsor de valor es necesario comentar que la dirección que puede seguir la tecnología puede ser desde la empresa hacia el resto del ecosistema generando valor a partir de disponibilizar tecnologías que no son de utilidad interna para la empresa. Estos seis impulsores de creación de valor, presentes en los procesos de innovación corporativos, tienen la capacidad de influir en la estrategia y organización de la empresa aumentando su habilidad de crear valor. El Proceso de Creación de Valor en las Empresas Luego se ha investigado la práctica de la gestión basada en valor que sostiene la necesidad de alinear la estrategia corporativa y el diseño de la organización con el fin de obtener retornos financieros superiores al resto de los competidores de manera sostenida, y finalmente crear valor a lo largo del tiempo. Se describe como los impulsores de creación de valor influyen en la creación y fortalecimiento de las ventajas competitivas de la empresa impactando y alineando su estrategia y organización. Durante la investigación se ha identificado que las opciones reales pueden utilizarse como una herramienta para gestionar entornos de innovación abierta que, por definición, tienen altos niveles de incertidumbre. Las opciones reales aportan una capacidad para la toma de decisiones de forma modular y flexible que pueden aplicarse al entorno corporativo. Las opciones reales han sido particularmente diseñadas para entender, estructurar y gestionar entornos de múltiples incertidumbres y por ello tienen una amplia aplicación en los entornos de innovación. Se analizan los usos potenciales de las opciones reales como complemento a los distintos instrumentos identificados en los Programas de Innovación Abierta. La Interacción Entre los Programas de Innovación Abierta, los Impulsores de Creación de Valor y el Proceso de Creación de Valor A modo de conclusión del presente trabajo se puede mencionar que se ha desarrollado un marco general de creación de valor en el entorno de los Programas de Innovación Abierta. Este marco general incluye tres elementos fundamentales. En primer lugar describe los elementos que se encuentran presentes en los Programas de Innovación Abierta, en segundo lugar como estos programas colaboran en la creación de los seis impulsores de creación de valor que se han identificado y finalmente en tercer lugar como estos impulsores impactan sobre la estrategia y la organización de la empresa para dar lugar a la creación de valor de forma sostenida. A través de un Programa de Innovación Abierta, se pueden desarrollar los impulsores de valor para fortalecer la posición estratégica de la empresa y su capacidad de crear de valor. Es lo que denominamos el marco de referencia para la creación de valor en un Programa de Innovación Abierta. Se presentará la idea que los impulsores de creación de valor pueden colaborar en generar una estrategia óptima que permita alcanzar un desempeño financiero superior y lograr creación de valor de la empresa. En resumen, se ha desarrollado un modelo de relación que describe el proceso de creación de valor en la empresa a partir de los Programas de Innovación Abierta. Para ello, se han identificado los impulsores de creación de valor y se ha descripto la interacción entre los distintos elementos del modelo. ABSTRACT In a world of constant, accelerating change innovation is fuel for business. Year after year, innovation allows firms to renew and, therefore, advance their long--‐term survival. Undoubtedly, innovation is a key element for the firms’ ability to create value over time. Companies often devote considerable effort and diverse resources to identify innovation alternatives that could fit into their strategy, culture, corporate goals and ambitions. Open innovation refers to a specific approach to innovate by collaborating with other firms operating within the same business ecosystem.2 The term open innovation was pioneered by Henry Chesbrough more than a decade ago to refer to this particular mode of driving corporate innovation. Open innovation is a new paradigm that has attracted academic and business interest for over a decade. Several cases of open innovation from different countries and from different economic sectors are included and reviewed in this document. The main objective of this study is to explain and develop a relationship model between open innovation and value creation. To this end, and as secondary objectives, we have explored the elements of an Open Innovation Program, the drivers of value creation, the process of value creation and, finally, the interaction between these three elements. As a final product of the research we have developed a general theoretical framework for establishing the connection between open innovation and value creation that facilitates the explanation of the interaction between the two. From the case studies we see that open innovation can encompass all sectors of the economy, multiple geographies and varying businesses – large companies, SMEs, including (even) start--‐ups – each with a different relevance within the ecosystem in which they participate. Elements of an Open Innovation Program We begin by listing and describing below the items that can be found in an Open Innovation Program. Many of such items have been identified through the review of relevant academic literature. Furthermore, in order to achieve a better understanding of Open Innovation, we have classified those aspects into four different categories according to the features they share. § Program Organization. An organizational structure must exist with a degree of interaction between the different members involved in the innovation process. This structure must be able to meet a number of previously established objectives. § Internal Talent. Internal talent plays a key role in the implementation and success of any Open Innovation program. An open innovation culture and leadership skills are essential for adopting either radical or incremental innovation. In fact, leadership is closely linked to organizational behavior and it is essential to promote open innovation. § Infrastructure. This category groups the elements related to the technological infrastructure required to carry out the program, including production processes and daily management tools. § Instruments. Finally, we list the instruments or vehicles used in the corporate environment to implement open innovation. Several instruments are available, such as corporate incubators, licensing agreements or venture capital. There has been a growing and renewed interest in the latter, both in academia and business circles. The use of corporate venture capital to sustain the development of the open innovation strategy brings ability, credibility, and technological support to the process. The combination of elements from these four categories, interacting in a coordinated way, makes it possible to create, enhance and develop value creation drivers that may impact the company’s strategy and organization and affect its financial performance over time. The Drivers of Value Creation After identifying describing and categorizing the different elements present in an Open Innovation Program our research examines the drivers of value creation. These can be defined as elements that enhance or determine the ability to create value in the business environment. As can be seen, these drivers can act as interacting points between the elements of the program and the process of value creation. The study identifies six drivers of value creation that might be found in an Open Innovation Program. § New Products and Services. The more direct and obvious driver of value creation in any Open Innovation Program is the ability to create new products and services. This is directly related to the company’s innovation process. § Access to Adjacent Markets. The innovation process can also serve as a source of value by granting access to adjacent markets through satisfying new needs for existing customers or attracting new customers from other markets. § Availability of Technologies. The availability of technology is in itself a driver for value creation. New technologies can either be complementary and/or can leverage existing technologies within the firm. They can partly transform certain elements of the company’s strategy. § External Talent Strategy. Incorporating an Open Innovation Program offers the opportunity to interact with other organizations operating in the same ecosystem and can therefore attract external skilled resources. Talent mobility is a unique feature of open innovation. § Becoming Part of a Virtuous Circle. The actions carried out in the environment by any of its members will also have a clear impact on value creation for the other participants. Participation in a virtuous ecosystem is thus a driver for value creation in an open innovation strategy. § Inside--‐out Technology. Value creation may also evolve by allowing other firms in the ecosystem to incorporate internally developed under--‐utilized technologies into their own innovation processes. These six drivers that are present in the innovation process can influence the strategy and the organization of the company, increasing its ability to create value. The Value Creation Process Value--‐based management is the management approach that requires aligning the corporate strategy and the organizational design to create value and obtain sustained financial returns (at least, higher returns than its competitors). We describe how the drivers of value creation can enhance corporate advantages by aligning its strategy and organization. During this study, we were able to determine that real options can be used as managing tools in open innovation environments which, by definition, have high uncertainty levels. Real options provide capability for flexible and modular decision--‐making in the business environment. In particular, real options have been designed for uncertainty management and, therefore, they may be widely applied in innovation environments. We analyze potential uses of real options to supplement the various instruments identified in the Open Innovation programs. The Interaction Between Open Innovation Programs, Value Creation drivers and Value Creation Process As a result of this study, we have developed a general framework for value creation in Open Innovation Programs. This framework includes three key elements. We first described the elements that are present in Open Innovation Programs. Next, we showed how these programs can boost six drivers of value creation that have been identified. Finally, we analyzed how the drivers impact on the strategy and organization of the company in order to lead to the creation of sustainable value. Through an Open Innovation Program, value drivers can be developed to strengthen a company’s strategic position and its ability to create value. That is what we call the framework for value creation in the Open Innovation Program. Value drivers can collaborate in generating an optimal strategy that helps foster a superior financial performance and a sustained value creation process. In sum, we have developed a relationship model that describes the process of creating value in a firm with an Open Innovation Program. We have identified the drivers of value creation and described how the different elements of the model interact with each other.

Hysteresis in transverse galloping: the role of the inflection points

Transverse galloping is here considered as a one-degree-of-freedom oscillator subjected to aerodynamic forces, which are described by using the quasi-steady hypothesis. The hysteresis of transverse galloping is also analyzed. Approximate solutions of the model are obtained by assuming that the aerodynamic and damping forces are much smaller than the inertial and stiffness ones. The analysis of the approximate solution, which is obtained by means of the method of Krylov–Bogoliubov, reveals the existing link between the hysteresis phenomenon and the number of inflection points at the aerodynamic force coefficient curve, Cy(α)Cy(α); CyCy and αα being, respectively, the force coefficient normal to the incident flow and the angle of attack. The influence of the position of these inflection points on the range of flow velocities in which hysteresis takes place is also analyzed.

Multiple feature points representation in target localization of wireless visual sensor networks

This paper discusses the target localization problem in wireless visual sensor networks. Additive noises and measurement errors will affect the accuracy of target localization when the visual nodes are equipped with low-resolution cameras. In the goal of improving the accuracy of target localization without prior knowledge of the target, each node extracts multiple feature points from images to represent the target at the sensor node level. A statistical method is presented to match the most correlated feature point pair for merging the position information of different sensor nodes at the base station. Besides, in the case that more than one target exists in the field of interest, a scheme for locating multiple targets is provided. Simulation results show that, our proposed method has desirable performance in improving the accuracy of locating single target or multiple targets. Results also show that the proposed method has a better trade-off between camera node usage and localization accuracy.